Question

It is May 1. The quoted price of a bond with a 30/360 day count and 12% per annum coupon in the United States is 105. It has a face value of 100 and pays coupons on April 1 and October 1. What is the cash price?
A. 106.00
B. 106.02
C.105.98
D. 106.04

Answer 1

Answer: option A is the correct option.

Cash price = 106.00

Explanation:

Cash price = quoted price + accrued interest

CP = Qp + I ..........................(1)

Quoted price = 105

Accrued interest = ?

STEP1 : FIND INTEREST;

Because the interest is not compounded

Accrued Interest = PRT ..........(2)

P= principal ( the face value)

R = rate per annum

T= period

P= 100

Since the period of payment of the face value was from April 1 to October 1 that means the period is 180 days, that means the 12% rate per annum (360 days), should be 6% rate per halve annum (180 days).

Therefore;

R = 6%

Since rate is applied every 30 days of the period which is 30/360 for an annum. Our period is 180 that's means rate will be applied to 30/180.

Therefore;

T = 30/180

Therefore using equation 2

I = 100 × 6% × (30/180) = 1.00

Accrued interest= 1.00

STEP 2: FIND CASH PRICE

using equation 1

Cash price = 105 + 1.00 = 106.00